Question

Conduct a test at the alpha equals0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2 . The sample data are x 1 equals 126 ​, n 1 equals 242 ​, x 2 equals 131 ​, and n 2 equals 313 .

(a) Choose the correct null and alternative hypotheses below.

A.

Upper H 0 : p 1 equals p 2

versus Upper H 1 : p 1 greater than p 2

B.

Upper H 0 : p 1 equals p 2

versus Upper H 1 : p 1 less than p 2

C.

Upper H 0 : p 1 equals 0

versus Upper H 1 : p 1 not equals 0

D.

Upper H 0 : p 1 equals p 2

versus Upper H 1 : p 1 not equals p 2

​(b) Determine the test statistic.

z0 =

nothing​(Round to two decimal places as​ needed.)

(c) Determine the​ P-value.

The​ P-value is?

.​(Round to three decimal places as​ needed.)

What is the result of this hypothesis​ test?

A.

Reject

the null hypothesis because there

is

sufficient evidence to conclude that

p 1 less than p 2

.

B.

Reject

the null hypothesis because there

is

sufficient evidence to conclude that

p 1 greater than p 2

.

C.

Do not reject the

alternative

hypothesis because there

is

sufficient evidence to conclude that

p 1 not equals p 2

.

D.

Do not reject

the null hypothesis because there

is not

sufficient evidence to conclude that

p 1 less than p 2

.

Answer 1

p-value = P(Z > TS)

= 0.0084

a)

Ho:p1 = p2

Ha: p1 > p2

option A) is correct

b)

z = 2.39

c)

p-value = 0.008

Conclusion

option B) Reject the null hypothesis because there is sufficient evidence to conclude that p1 > p 2

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